Consider the equation y=1/4(x+2)(x-6). is it easier to find the x-intercepts of this equation or the vertex? why?

x intercepts are easier. They are almost just read.

Step-by-step explanation:

The x intercepts are easier to find. You can almost just read them.

x + 2 = 0     Subtract 2 from both sides.

x = - 2          Answer

x - 6 = 0      Add 6 to both sides.

x = 6            Answer

So the x intercepts are (6,0) and (-2,0)

Now to the vertex. You could average the two x intercepts.  But that will give you only the x value of the vertex. (6 - 2)/2 = (4)/2 = 2

But you still have to get the y value.

y(2) = (1/4)*(x + 2)( x - 6)            Substitute 2 in for both xs

y(2) = (1/4)* (2 + 2) (2 - 6)          Combine the terms

y(2) = (1/4) * 4 * - 4                     multiply the 1/4 * 4 which gives 1

y(2) = 1 *- 4 = - 4

The vertex is (2,-4)

Note: If you do this the long way. The 1/4 has to be taken into account. Here we don't have to. The final result is

y = (1/4)(x - 2)^2 - 4

and even then, the - 4 gives some trouble. The x intercepts are much easier.

answer: expected value of x = 1.0

step-by-step explanation:

p(x=0) = 0.25

p(x=1) = 0.50

p(x=2) = 0.25

expected value for x = 0×0.25 + 1×0.5 + 2×0.25 = 1.0